Geodesic
Cubature formulae for Besov classes
Izvestiya. Mathematics , Tome 61 (1997) no. 2, pp. 259-283.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is devoted to an investigation of optimal cubature formulae for Besov classes of functions with restrictions on the mixed difference. This study is a continuation of papers [1] and [2]. In this paper we find the exact order of the error of the cubature formula using the values of the function at particular points. 
@article{IM2_1997_61_2_a1,
     author = {V. V. Dubinin},
     title = {Cubature formulae for {Besov} classes},
     journal = {Izvestiya. Mathematics },
     pages = {259--283},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_2_a1/}
}
TY  - JOUR
AU  - V. V. Dubinin
TI  - Cubature formulae for Besov classes
JO  - Izvestiya. Mathematics 
PY  - 1997
SP  - 259
EP  - 283
VL  - 61
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1997_61_2_a1/
LA  - en
ID  - IM2_1997_61_2_a1
ER  - 
%0 Journal Article
%A V. V. Dubinin
%T Cubature formulae for Besov classes
%J Izvestiya. Mathematics 
%D 1997
%P 259-283
%V 61
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1997_61_2_a1/
%G en
%F IM2_1997_61_2_a1
V. V. Dubinin. Cubature formulae for Besov classes. Izvestiya. Mathematics , Tome 61 (1997) no. 2, pp. 259-283. http://geodesic.mathdoc.fr/item/IM2_1997_61_2_a1/

[1] Dubinin V. V., “Ob optimalnykh kvadraturnykh formulakh dlya klassov funktsii s ogranichennoi smeshannoi raznostyu”, Matem. zametki, 49:1 (1991), 149–151 | MR | Zbl

[2] Dubinin V. V., “Kvadraturnye formuly dlya klassov funktsii s ogranichennoi smeshannoi raznostyu”, Matem. sb., 183:7 (1992), 23–34 | MR | Zbl

[3] Dubinin V. V., Optimalnye kubaturnye formuly dlya klassov funktsii s ogranicheniyami, nalozhennymi na smeshannuyu raznost, Dis. ...kand. fiz.-mat. nauk, 1993 | MR | Zbl

[4] Frolov K. K., Kvadraturnye formuly na klassakh funktsii, Dis. ...kand. fiz.-mat. nauk, VTs AN SSSR, M., 1979

[5] Temlyakov V. N., “Ob odnom prieme polucheniya otsenok snizu pogreshnostei kvadraturnykh formul”, Matem. sb., 181:10 (1990), 1403–1413 | MR | Zbl

[6] Frolov K. K., “Otsenki sverkhu pogreshnostei kvadraturnykh formul na klassakh funktsii”, DAN SSSR, 231:4 (1976), 818–821 | MR | Zbl

[7] Bakhvalov N. S., “Otsenki snizu asimptoticheskikh kharakteristik klassov funktsii s dominiruyuschei smeshannoi proizvodnoi”, Matem. zametki, 12:6 (1972), 655–664 | MR | Zbl

[8] Bykovskii V. A., O pravilnom poryadke pogreshnosti optimalnykh kubaturnykh formul v prostranstvakh s dominiruyuschei proizvodnoi i kvadratichnykh otkloneniyakh setok, Preprint Dalnevostochnogo nauchnogo tsentra AN SSSR, 1985, 3–31

[9] Temlyakov V. N., Priblizhenie funktsii s ogranichennoi smeshannoi proizvodnoi, Tr. MIAN, CLXXVIII, Nauka, M., 1986 | MR | Zbl

[10] Nikolskii S. M., “Neravenstva dlya tselykh funktsii konechnoi stepeni i ikh primenenie v teorii differentsiruemykh funktsii mnogikh peremennykh”, Tr. MIAN, 38, Izd-vo AN SSSR, M., 1951, 244–278 | MR | Zbl

[11] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1977 | MR

[12] Amanov T. I., Prostranstva differentsiruemykh funktsii s dominiruyuschei smeshannoi proizvodnoi, Nauka KazakhSSR, Alma-Ata, 1976 | MR